r = 8sin(Theta). Write an equation in rectangular coordinates.

Question

irishboy123 · Answer

what are x and y in polar?!?!

anonymous · Answer

"Transform the polar equation to an equation in rectangular coordinates" is all it says ...

anonymous · Answer

but everyone is telling me to use this formula:
 x = rcosθ 
y = rsinθ 
x² + y² = r²

irishboy123 · Answer

yes

that's right

so $r = 8 \sin( \theta)$ is the same as

$\sqrt{x^2 + y^2} = 8\dfrac{ y}{\sqrt{x^2 + y^2}}$

anonymous · Answer

Yes but I am not sure how to solve this..

irishboy123 · Answer

multiply each side by $\sqrt{x^2 + y^2}$

irishboy123 · Answer

$$\sqrt{x^2 + y^2} * \sqrt{x^2 + y^2}  = 8\dfrac{ y}{\sqrt{x^2 + y^2}}*\sqrt{x^2 + y^2} $$

anonymous · Answer

??

irishboy123 · Answer

$$\sqrt{x^2 + y^2}  * \sqrt{x^2 + y^2}  = x^2 + y^2 $$

right?!

irishboy123 · Answer

and

$$\dfrac{ y}{\sqrt{x^2 + y^2}}*\sqrt{x^2 + y^2} = y$$

yes?